This paper proposes a full-rate cooperative scheme adapted to the slow fading semi-orthogonal multiple access relay channel (MARC). It is assumed that the sources transmit on orthogonal channels and the relay is half duplex transmitting on the same channels as the one of the sources. The sources employ LDPC to encode their messages before transmitting them, while the relay uses a simple demodulate-and-forward strategy to transmit the combination of the received codewords. The presence of the relay does not affect the time-scheduling of the sources. Therefore, this scheme is backward compatible to existing non-cooperative systems. In order to cancel the interference at the destination, we propose a joint network-channel decoder that uses maximum a posteriori (MAP) detection and channel decoding. Through numerical results, we show the benefits of joint network-channel decoder. We also show that the proposed scheme significantly outperforms, in terms of BER, the non-cooperative system as well as the classical relay-assisted orthogonal channel network and that it achieves the maximum code diversity.